Hmmm... that's weird. You could either report that as a bug or try to browse the recent pull requests in search for what could've Wikia updated so it suddenly stopped working without Flash. I couldn't find anything myself.
Just had a look at network requests and found two for Flash... (an example) but it's blank to me?
Flash is often used for video or interactive ads because it is one of the few ways advertisers can send out videos that aren't easy to copy (or steal). Although truthfully, it is a dumb solution. Anything that can be seen can be copied.
I also noticed the flash when running wikia through webpagetest.com. They use up a considerable portion of the bandwith, and make pages take longer to load.
I've noticed there's a tracking flash (like a tracking pixel, but a flash app) on lots of Wikia pages. It's not an ad. It doesn't display anything.